Time-shift imaging condition Paul Sava & Sergey Fomel Bureau of Economic Geology University of Texas at Austin

Imaging condition Image Source wavefield Receiver wavefield Wavefield reconstruction Imaging sketch S R Angle decomposition Angle-dependent reflectivity

Wavefield reconstruction

Wavefield reconstruction Source wavefield Receiver wavefield S R Reverse-time extrapolation Kirchhoff integral Wavefield extrapolation …

Imaging condition

Conventional imaging condition source wavefield receiver wavefield image position time

Conventional imaging condition Claerbout (1985) position time

Conventional imaging condition position frequency

distance depth Conventional imaging condition example

Space-shift imaging condition source wavefield receiver wavefield image position time space-shift

Space-shift imaging condition position time space-shift Rickett & Sava (2002) Biondi & Symes (2004) Sava & Fomel (2005)

Space-shift imaging condition position frequency space-shift

distance depth Space-shift imaging condition example

Time-shift imaging condition source wavefield receiver wavefield image position time time-shift

Time-shift imaging condition position time time-shift

Time-shift imaging condition position frequency time-shift

Time-shift imaging condition example distance depth

distance  h Imaging condition: example 1 depth space-shifttime-shift

 h distance Imaging condition: example 2 depth space-shifttime-shift

Imaging condition summary time-shift space-shift

Angle decomposition

pmpm phph psps prpr  Angle decomposition Space-shiftTime-shift

pmpm phph psps prpr  Vector geometry Space-shiftTime-shift

Image-space angle decomposition Space-shiftTime-shift

Angle decomposition algorithm Space-shiftTime-shift

distance depth Space-shift angle decomposition example

Time-shift angle decomposition example distance depth

distance  Angle decomposition: example 1 depth space-shifttime-shift

distance  Angle decomposition: example 2 depth space-shifttime-shift

distance  Correct velocity depth space-shifttime-shift

distance  Incorrect velocity depth space-shifttime-shift

 Angle decomposition summary depth distance  h depth

 Angle decomposition summary depth distance  h depth

Summary Imaging condition and angle-decomposition –time-shifts of source/receiver wavefields –cheaper than space-shift imaging –storage –computations –wide applicability –migration by wavefield extrapolation –Kirchhoff migration –reverse-time migration